The answer in question is to Facebook PHP-SDK: getUser() always returns 0.
getUser() returning 0 isn't a specific problem. I wrote a walktrough on how to examine it and added solutions (also with answered links from Stack Overflow).
There are a lot of people asking the same question and questions weren't answered or solved(or weren't deleted, of course).
So I posted this answer on each question. My posts (all of them) were deleted. Why? I thought it might be useful for people who experience same problem.